My problem appears in solving volume of body, defined by this equation

(x^2+y^2+z^2) = 4a(x^2+y^2)

a=constant

Printable View

- Jun 12th 2012, 03:35 PMVektorCone volume-triple integral
My problem appears in solving volume of body, defined by this equation

(x^2+y^2+z^2) = 4a(x^2+y^2)

a=constant - Jun 12th 2012, 07:43 PMDeMathRe: Cone volume-triple integral
I think, that you mean this equation .

We consider the case and multiply by 2 the integral (since this body is symmetrical about the plane ).

Find the body's proection on the plane :

So, (As you can see, this projection is a circle whose radius is equal to ).

We write a set , which limits the surface :

Convert to the cylindrical coordinates .

So, finally you have

- Jun 13th 2012, 07:04 AMVektorRe: Cone volume-triple integral
thank you very very much, you solved my problem :)